Ohio Resource Center
Lessons
Can You Can a Can?
Discipline
Mathematics
7, 8
Professional Commentary

Students determine the dimensions of a can that has minimum surface area for a given volume. Reviewers liked the systematic approach described in the lesson and noted that this activity leads naturally into the minimum of a function. An activity sheet and extensions of the lesson are included. (sw)

Common Core State Standards for Mathematics
Geometry
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
7.G.B.4
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
7.G.B.6
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Functions
Define, evaluate, and compare functions.
Use functions to model relationships between quantities.
8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Geometry
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
8.G.C.9
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Ohio Mathematics Academic Content Standards (2001)
Measurement Standard
Benchmarks (8–10)
B.
Use formulas to find surface area and volume for specified three-dimensional objects accurate to a specified level of precision.
E.
Estimate and compute various attributes, including length, angle measure, area, surface area and volume, to a specified level of precision.
3.
Use appropriate levels of precision when calculating with measurements.
10.
Use conventional formulas to find the surface area and volume of prisms, pyramids and cylinders and the volume of spheres and cones to a specified level of precision.
Patterns, Functions and Algebra Standard
Benchmarks (8–10)
D.
Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.
8.
Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems.